Answer:
option4 : 0.4
Step-by-step explanation:
![Sin N = \frac{Opposite}{hypotenuse}](https://tex.z-dn.net/?f=Sin%20N%20%3D%20%5Cfrac%7BOpposite%7D%7Bhypotenuse%7D)
![sin 7 = \frac{x}{3.4}\\\\3.4 \times sin 7 = x \\\\3.4 \times 0.122 = x \\x = 0.41](https://tex.z-dn.net/?f=sin%207%20%3D%20%5Cfrac%7Bx%7D%7B3.4%7D%5C%5C%5C%5C3.4%20%5Ctimes%20sin%207%20%3D%20x%20%5C%5C%5C%5C3.4%20%5Ctimes%200.122%20%3D%20x%20%5C%5Cx%20%3D%200.41)
Answer:
A and B
Step-by-step explanation:
Given
List of given options
Required
Which will correctly take 3 to fill the blank
Represent the blanks with x
Option A:
![x : 4 = 12 : 16](https://tex.z-dn.net/?f=x%20%3A%204%20%3D%2012%20%3A%2016)
Convert to fractions
![\frac{x}{4} = \frac{12}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D%20%3D%20%5Cfrac%7B12%7D%7B16%7D)
Multiply through by 4
![4 * \frac{x}{4} = 4 * \frac{12}{16}](https://tex.z-dn.net/?f=4%20%2A%20%5Cfrac%7Bx%7D%7B4%7D%20%3D%204%20%2A%20%5Cfrac%7B12%7D%7B16%7D)
![x = \frac{48}{16}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B48%7D%7B16%7D)
![x = 3](https://tex.z-dn.net/?f=x%20%3D%203)
Option B:
![1 : 5= x : 15](https://tex.z-dn.net/?f=1%20%3A%205%3D%20x%20%3A%2015)
Convert to fraction;
![\frac{1}{5} = \frac{x}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%3D%20%5Cfrac%7Bx%7D%7B15%7D)
Multiply through by 15
![15 * \frac{1}{5} = \frac{x}{15} * 15](https://tex.z-dn.net/?f=15%20%2A%20%5Cfrac%7B1%7D%7B5%7D%20%3D%20%5Cfrac%7Bx%7D%7B15%7D%20%2A%2015)
![15 * \frac{1}{5} = x](https://tex.z-dn.net/?f=15%20%2A%20%5Cfrac%7B1%7D%7B5%7D%20%3D%20x)
![3 = x](https://tex.z-dn.net/?f=3%20%3D%20x)
![x = 3](https://tex.z-dn.net/?f=x%20%3D%203)
Option C:
![x : 1 = 12 : 3](https://tex.z-dn.net/?f=x%20%3A%201%20%3D%2012%20%3A%203)
Convert to fraction
![\frac{x}{1} = \frac{12}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B1%7D%20%3D%20%5Cfrac%7B12%7D%7B3%7D)
![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
Option D
![15:x = 3:1](https://tex.z-dn.net/?f=15%3Ax%20%3D%203%3A1)
Convert to fraction
![\frac{15}{x} = \frac{3}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7Bx%7D%20%3D%20%5Cfrac%7B3%7D%7B1%7D)
Cross Multiply
![3 * x = 15 * 1](https://tex.z-dn.net/?f=3%20%2A%20x%20%3D%2015%20%2A%201)
![3 * x = 15](https://tex.z-dn.net/?f=3%20%2A%20x%20%3D%2015)
Divide through by 3
![x = 5](https://tex.z-dn.net/?f=x%20%3D%205)
From the above calculations.
<em>Option A and B can be filled with 3</em>
Question #1:
To find the percentage of boy's in the class, divide.
9 / 36 = 0.25
0.25 * 100% = 25% (boys in the class)
We can write this proportion as 9/36 since this is the same as 25%.
_________
Question #2:
We know that the ear buds in both options cost $125.
The earbuds online are on a 20% discount.
The earbuds in store are on a 90$ sale
Lets find the discount for the online pair.
20% = 0.2
125 * 0.2 = 25
125 - 25 = $100 (price after discount)
After solving we can see that the earbuds in store are a better price. So, you will purchase the ear buds in store.
_________
Best Regards,
Wolfyy :)
Here , we are provided with a table which shows 5 consecutive terms of an arithmetic sequence . But before solving further , let's recall that ;
The n'th term of a Arithmetic Sequence let's say it be
is given by ;
Where , <u>d</u> is the common difference
Now , here we are given with ;
We have to find the 2nd , 3rd and 4th term respectively ,
Now , by using the above formula , 5th term can be written as ;
Putting the values and transposing 1st term to RHS , we have ;
Now , as we got the common difference , so we can find out the missing terms now ;
![{: \implies \quad \sf T_{2}= 8 +d}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Csf%20T_%7B2%7D%3D%208%20%2Bd%7D)
![{: \implies \quad \sf T_{2}= 8-3}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Csf%20T_%7B2%7D%3D%208-3%7D)
![{: \implies \quad \bf \therefore \: T_{2}= 5}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Cbf%20%5Ctherefore%20%5C%3A%20%20T_%7B2%7D%3D%205%7D)
Now
![{: \implies \quad \sf T_{3}= 8 +2d}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Csf%20T_%7B3%7D%3D%208%20%2B2d%7D)
![{: \implies \quad \sf T_{3}= 8-6}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Csf%20T_%7B3%7D%3D%208-6%7D)
![{: \implies \quad \bf \therefore \: T_{3}= 2}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Cbf%20%5Ctherefore%20%5C%3A%20%20T_%7B3%7D%3D%202%7D)
Also ,
![{: \implies \quad \sf T_{4}= 8 +3d}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Csf%20T_%7B4%7D%3D%208%20%2B3d%7D)
![{: \implies \quad \sf T_{4}= 8-9}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Csf%20T_%7B4%7D%3D%208-9%7D)
![{: \implies \quad \bf \therefore \: T_{4}= -1}](https://tex.z-dn.net/?f=%7B%3A%20%5Cimplies%20%5Cquad%20%5Cbf%20%5Ctherefore%20%5C%3A%20%20T_%7B4%7D%3D%20-1%7D)
Now , The given table can be written as ;
![{\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \bf n & \sf 1 & 2 & 3 & 4 & 5 \\ \cline{1-6} \bf T_{n} & \sf 8 & 5 & 2 & -1 & -4 \end{array}}](https://tex.z-dn.net/?f=%7B%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%5Ccline%7B1-6%7D%20%5Cbf%20n%20%26%20%5Csf%201%20%26%202%20%26%203%20%26%204%20%26%205%20%5C%5C%20%5Ccline%7B1-6%7D%20%5Cbf%20T_%7Bn%7D%20%26%20%5Csf%208%20%26%205%20%26%202%20%26%20-1%20%26%20-4%20%5Cend%7Barray%7D%7D)
Note :- Kindly view the answer from web , if you're not able to see the full answer from here ;
brainly.com/question/26750175